Gravitational self-interaction near black holes?

Hello,

I came across a rather odd notion concerning black holes the other
day. Seeing as gravitational interaction is commonly believed to act
at light speed, how can a black hole exert any gravitational influence
on its surroundings? Surely for this to be possible gravity shouldn't
be able to act upon itself?

I'm not sure whether a gravitational field can act upon itself at all.
I like to think I'm fairly familiar with most astrophysical concepts,
but this keeps puzzling me. Any ideas on the subject?

Kind regards,

Christiaan Brinkerink